A 4 lbm mixture of 50% argon and 50% nitrogen by mole is in a tank at 300 psia, 320 R. How large is the volume using a model of (a) ideal gas and (b) Kays rule with generalized compressibility charts.

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Accepted Answer

a) Ideal gas mixture
Eq.11.5:

[latex]\begin{aligned}& M _{\operatorname{mix}}=\sum y _{ i } M _{ i }=0.5 imes 39.948+0.5 imes 28.013=33.981 \& R =1545.36 / 33.981=45.477 lbf - ft / lbm - R \& V =\frac{ mRT }{ P }=\frac{4 imes 45.477 imes 320}{300 imes 144} \frac{ lbf - ft }{ psi imes in ^{2} / ft ^{2}}= 1 . 3 4 7 \mathrm { ft } ^ { 3 }\end{aligned}[/latex]

b) Kay’s rule Eq.12.84

[latex]\begin{aligned}& P _{ c ext { mix } }=0.5 imes 706+0.5 imes 492=599 psia \& T _{ c ext { mix }}=0.5 imes 271.4+0.5 imes 227.2=249.3 R\end{aligned}[/latex]

Reduced properties: [latex]P _{ r }=\frac{300}{599}=0.50, \quad T _{ r }=\frac{320}{249.3}=1.284[/latex]

Fig. D.1: Z = 0.92

[latex]V = Z \frac{ m \overline{ R } T }{ M _{\operatorname{mix}} P }= Z V _{ ID gas }=0.92 imes 1.347= 1 . 2 4 ft ^{3}[/latex]

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Eq.11.5: [latex]M_{\operatorname{mix}}=\frac{m_{ tot }}{n_{ tot }}=\frac{\sum n_{i} M_{i}}{n_{ tot }}=\sum y_{i} M_{i}[/latex]

Eq.12.84 : [latex]\left(P_{c} ight)_{\operatorname{mix}}=\sum_{i} y_{i} P_{c i}, \quad\left(T_{c} ight)_{\operatorname{mix}}=\sum_{i} y_{i} T_{c i}[/latex]

Question 12.179E: A 4 lbm mixture of 50% argon and 50% nitrogen by mole is in ...

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